In [4], Kunen used iterated ultrapowers to show that ifUis a normalκ-complete nontrivial ultrafilter on a cardinalκthenL[U], the class of sets constructive fromU, has only the ultrafilterU∩L[U] and this ultrafilter depends only onκ. In this paper we extend Kunen's methods to arbitrary sequencesUof ultrafilters and obtain generalizations of these results. In particular we answer Problem 1 of Kunen and Paris [5] which asks whether the number of ultrafilters onκcan be intermediate between 1 and 22κ. If there is a normalκ-complete ultrafilterUonκsuch (...) that {α <κ: α is measurable} ∈Uthen there is an inner model with exactly two normal ultrafilters onκ, and ifκis super-compact then there are inner models havingκ+ +,κ+or any cardinal less than or equal toκnormal ultrafilters.These methods also show that several properties ofLwhich had been shown to hold forL[U] also hold forL[U]: using an idea of Silver we show that inL[U] the generalized continuum hypothesis is true, there is a Souslin tree, and there is awell-ordering of the reals. In addition we generalize a result of Kunen to characterize the countaby complete ultrafilters ofL[U]. (shrink)

Continuing William Mitchell's investigations of how we understand, reason about, anduse images, The Reconfigured Eye provides the first systematic, critical analysis of the digitalimaging revolution.

We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem. Suppose κ is a singular strong limit cardinal and 2κ λ where λ is not the successor of a cardinal of cofinality at most κ. If cf > ω then it follows that o λ, and if cf = ωthen either o λ or {α: K o α+n} is confinal in κ for (...) each n ε ω.We also prove several results which extend or are related to this result, notably Theorem. If 2ω ω1 then there is a sharp for a model with a strong cardinal.In order to prove these theorems we give a detailed analysis of the sequences of indiscernibles which come from applying the covering lemma to nonoverlapping sequences of extenders. (shrink)

We give a short proof of a lemma which generalizes both the main lemma from the original construction in the author’s thesis of a model with no ω2-Aronszajn trees, and also the “Key Lemma” in Hamkins’ gap forcing theorems. The new lemma directly yields Hamkins’ newer lemma stating that certain forcing notions have the approximation property.

An outline is given of the proof that the consistency of a κ⁺-Mahlo cardinal implies that of the statement that I[ω₂] does not include any stationary subsets of Cof(ω₁). An additional discussion of the techniques of this proof includes their use to obtain a model with no ω₂-Aronszajn tree and to add an ω₂-Souslin tree with finite conditions.

Is there a dominant global image—call it a world picture—that links the Occupy movement to the Arab Spring? Or is there any single image that captures and perhaps even motivated the widely noticed synergy and infectious mimicry between Tahrir Square and Zuccotti Park?

We use a $\kappa^{+}-Mahlo$ cardinal to give a forcing construction of a model in which there is no sequence $\langle A_{\beta} : \beta \textless \omega_{2} \rangle$ of sets of cardinality $\omega_{1}$ such that $\{\lambda \textless \omega_{2} : \existsc \subset \lambda & (\bigcupc = \lambda otp(c) = \omega_{1} & \forall \beta \textless \lambda (c \cap \beta \in A_{\beta}))\}$ is stationary.

The rubric “The Late Derrida,” with all puns and ambiguities cheerfully intended, points to the late work of Jacques Derrida, the vast outpouring of new writing by and about him in the period roughly from 1994 to 2004. In this period Derrida published more than he had produced during his entire career up to that point. At the same time, this volume deconstructs the whole question of lateness and the usefulness of periodization. It calls into question the “fact” of his (...) turn to politics, law, and ethics and highlights continuities throughout his oeuvre. The scholars included here write of their understandings of Derrida’s newest work and how it impacts their earlier understandings of such classic texts as Glas and Of Grammatology . Some have been closely associated with Derrida since the beginning—both in France and in the United States—but none are Derrideans. That is, this volume is a work of critique and a deep and continued engagement with the thought of one of the most significant philosophers of our time. It represents a recognition that Derrida’s work has yet to be addressed—and perhaps can never be addressed—in its totality. (shrink)

We construct, assuming that there is no inner model with a Woodin cardinal but without any large cardinal assumption, a model Kc which is iterable for set length iterations, which is universal with respect to all weasels with which it can be compared, and is universal with respect to set sized premice.

Despite the salient experience of encoding threatening events, these memories are prone to distortions and often non-veridical from encoding to recall. Further, threat has been shown to preferentially disrupt the binding of event details and enhance goal-relevant information. While extensive work has characterised distinctive features of emotional memory, research has not fully explored the influence threat has on temporal memory, a process putatively supported by the binding of event details into a temporal context. Two primary competing hypotheses have been proposed; (...) that threat can impair or enhance temporal memory. We analysed two datasets to assess temporal memory for an in-person haunted house experience. In study 1, we examined the temporal structure of memory by characterising memory contiguity in free recall as a function of individual levels of heart rate as a proxy of threat. In study 2, we replicated marginal findings of threat-related increases in memory contiguity found in study 1. We extended these findings by showing threat-related increases in recency discriminations, an explicit test of temporal memory. Together, these findings demonstrate that threat enhances temporal memory regarding free recall structure and during explicit memory judgments. (shrink)

If there is no inner model with a cardinal κ such that o(κ) = κ ++ then the set K ∩ H ω 1 is definable over H ω 1 by a Δ 4 formula, and the set $\{J_\alpha[\mathscr{U}]: \alpha of countable initial segments of the core model K = L[U] is definable over H ω 1 by a Π 3 formula. We show that if there is an inner model with infinitely many measurable cardinals then there is a model (...) in which $\{J_\alpha [\mathscr{U}]: \alpha is not definable by any Σ 3 formula, and K ∩ H ω 1 is not definable by any boolean combination of Σ 3 formulas. (shrink)

We reprove Gitik's theorem that if the GCH holds and o(κ) = κ + 1 then there is a generic extension in which κ is still measurable and there is a closed unbounded subset C of κ such that every $\nu \in C$ is inaccessible in the ground model. Unlike the forcing used by Gitik. the iterated forcing $R_{\lambda +1}$ used in this paper has the property that if λ is a cardinal less then κ then $R_{\lambda + 1}$ can (...) be factored in V as $R_{\kappa + 1} = R_{\lambda + 1} \times R_{\lambda + 1, \kappa}$ where $\mid R_{\lambda +1}\mid \leq \lambda^+$ and $R_{\lambda + 1, \kappa}$ does not add any new subsets of λ. (shrink)

A tension between perspectives that emphasize deterministic versus stochastic processes has sparked controversy in ecology since pre-Darwinian times. The most recent manifestation of the contrasting perspectives arose with Hubbell’s proposed “neutral theory”, which hypothesizes a paramount role for stochasticity in ecological community composition. Here we shall refer to the deterministic and the stochastic perspectives as the niche-based and neutral-based research programs, respectively. Our goal is to represent these perspectives in the context of Lakatos’ notion of a scientific research program. We (...) argue that the niche-based program exhibits all the characteristics of a robust, progressive research program, including the ability to deal with disconfirming data by generating new testable predictions within the program. In contrast, the neutral-based program succeeds as a mathematical tool to capture, as epiphenomena, broad-scale patterns of ecological communities but appears to handle disconfirming data by incorporating hypotheses and assumptions from outside the program, specifically, from the niche-based program. We conclude that the neutral research program fits the Lakatosian characterization of a degenerate research program. (shrink)

We reprove Gitik’s theorem that if the GCH holds and $o=\gk+1$ then there is a generic extension in which $\gk$ is still measurable and there is a closed unbounded subset C of $\gk$ such that every $ν\in C$ is inaccessible in the ground model. Unlike the forcing used by Gitik, the iterated forcing $\radin\gl+1$ used in this paper has the property that if $\gl$ is a cardinal less then $\gk$ then $\radin\gl+1$ can be factored in V as $\radin\gk+1=\radin\gl+1\times\radin\gl+1,\gk$ where $\card{\radin\gl+1}\le\gl+$ (...) and $\radin\gl+1,\gk$ does not add any new subsets of $\gl$. (shrink)

Mitchell, W.J., An infinitary Ramsey property, Annals of Pure and Applied Logic 57 151–160. We prove that the consistency of a measurable cardinal implies the consistency of a cardinal κ>+ satisfying the partition relations κ ω and κ ωregressive. This result follows work of Spector which uses the same hypothesis to prove the consistency of ω1 ω. We also give some examples of partition relations which can be proved for ω1 using the methods of Spector but cannot be proved for (...) cardinals κ>+ without a much stronger hypothesis. (shrink)

We use a κ+-Mahlo cardinal to give a forcing construction of a model in which there is no sequence 〈 Aγ:γ<ω2 〉 of sets of cardinality ω1 such that {λ<ω2:∃ c⊂λ =ω1&∀γ<λ )} is stationary.

Assume that there is no transitive class model of [Formula: see text] with a Woodin cardinal. Let [Formula: see text] be a singular ordinal such that [Formula: see text] and [Formula: see text]. Suppose [Formula: see text] is a regular cardinal in K. Then [Formula: see text] is a measurable cardinal in K. Moreover, if [Formula: see text], then [Formula: see text].

This paper will introduce a new model for Linear Logic, the IE model . Intuitively the model assumes there is a global environment which is divided up into an internal resource and an external resource. Such an assumption makes for an elementary definition of linear negation. The model results in a fairly natural semantics for the multiplicative operators and the constants of Linear Logic. A particular example of the model is given which gives a proper technical account of the cigarette (...) example. (shrink)

If there is no inner model with a cardinal $\kappa$ such that $o = \kappa^{++}$ then the set $K \cap H_{\omega_1}$ is definable over H$_{\omega_1}$ by a $\Delta_4$ formula, and the set $\{J_\alpha[\mathscr{U}] : \alpha < \omega_1\}$ of countable initial segments of the core model $K = L[\mathscr{U}]$ is definable over $H_{\omega_1}$ by a $\Pi_3$ formula. We show that if there is an inner model with infinitely many measurable cardinals then there is a model in which $\{J_\alpha [\mathscr{U}] : \alpha (...) < \omega_1\}$ is not definable by any $\Sigma_3$ formula, and $K \cap H_{\omega_1}$ is not definable by any boolean combination of $\Sigma_3$ formulas. (shrink)