We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly -game-closed forcings. PFA can be destroyed by a strongly -game-closed forcing but not by an ω2-closed.

We show that for any infinite cardinal κ, every strongly $(\kappa + 1)-strategically$ closed poset is strongly $\kappa^+-strategically$ closed if and only if $AP_\kappa$ (the approachability property) holds, answering the question asked in [5]. We also give a complete classification of strengths of strategic closure properties and that of strong strategic closure properties respectively.

In this paper we show that the Proper Forcing Axiom is preserved under forcing over any poset PP with the following property: In the generalized Banach–Mazur game over PP of length , Player II has a winning strategy which depends only on the current position and the ordinal indicating the number of moves made so far. By the current position we mean: The move just made by Player I for a successor stage, or the infimum of all the moves made (...) so far for a limit stage. As a consequence of this theorem, we introduce a weak form of the square principle and show that it is consistent with PFA. (shrink)

We introduce properties of Boolean algebras which are closely related to the existence of winning strategies in the Banach‐Mazur Boolean game. A σ‐short Boolean algebra is a Boolean algebra that has a dense subset in which every strictly descending sequence of length ω does not have a nonzero lower bound. We give a characterization of σ‐short Boolean algebras and study properties of σ‐short Boolean algebras. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

We introduce properties of Boolean algebras which are closely related to the existence of winning strategies in the Banach-Mazur Boolean game. A σ-short Boolean algebra is a Boolean algebra that has a dense subset in which every strictly descending sequence of length ω does not have a nonzero lower bound. We give a characterization of σ-short Boolean algebras and study properties of σ-short Boolean algebras.

We show that strongly compact cardinals and MM are sensitive to $\lambda$-closed forcings for arbitrarily large $\lambda$. This is done by adding ‘regressive' $\lambda$-Kurepa trees in either case. We argue that the destruction of regressive Kurepa trees requires a non-standard application of MM. As a corollary, we find a consistent example of an $\omega_2$-closed poset that is not forcing equivalent to any $\omega_2$-directed-closed poset.

Humans are always interested in distinguishing natural and artificial entities although there is no sharp demarcation between the two categories. Surprisingly, things do not improve when the second type of entities is restricted to the arguably more constrained realm of physical technical artifacts. This paper helps to clarify the relationship between natural entities and technical artifacts by developing a conceptual landscape within which to analyze these notions. The framework is developed by studying three definitions of technical artifact which arise from (...) different perspectives. All these perspectives share two intuitions: that technical artifacts are physical objects that exist by human intervention; and that technical artifacts are entities to be contrasted to natural entities. Yet the perspectives are different in the way they spell out these intuitions: the relevant human intervention may range from intentional selection to intentional production; and the contrast between technical artifacts and natural entities may be introduced by a constitution relation or by defining properties that set technical artifacts apart. The three perspectives are compared and their similarities and dissimilarities are explored with the help of ontological analysis. (shrink)

明治大学文学部は、2018年4月に哲学専攻を新設した。いま、なぜ、哲学なのか?アジアにとって、哲学とは何か?理論とプラクティスが、西洋と東洋がクロスする新しい場から5名の創設メンバーが贈る“知”のスタ ーティングガイド。.

König, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of a higher Souslin tree from the strong guessing principle.Complementary to the author’s work on the validity of diamond and non-saturation at the successor of singulars, we deal here with a successor of regulars. It is established that even the non-strong guessing principle entails non-saturation, and that, assuming the necessary cardinal arithmetic configuration, entails a diamond-type principle which suffices for the construction of (...) a higher Souslin tree.We also establish the consistency of GCH with the failure of the weakest form of generalized club guessing. This, in particular, settles a question from the original paper. (shrink)