Forcing with adequate sets of models as side conditions

Mathematical Logic Quarterly 63 (1-2):124-149 (2017)
  Copy   BIBTEX

Abstract

We present a general framework for forcing on ω2 with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable models as being membership related up to a large initial segment. We give several examples of this type of forcing, including adding a function on ω2, adding a nonreflecting stationary subset of, and adding an ω1‐Kurepa tree.

Categories

Add categories

Keywords

Reprint years

DOI

10.1002/malq.201400022

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,923

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Strongly adequate sets and adding a club with finite conditions.John Krueger - 2014 - Archive for Mathematical Logic 53 (1-2):119-136.
Forcing with Sequences of Models of Two Types.Itay Neeman - 2014 - Notre Dame Journal of Formal Logic 55 (2):265-298.
Essential Forcing Generics.Stephanie Cawthorne & David Kueker - 2000 - Notre Dame Journal of Formal Logic 41 (1):41-52.
Computability in structures representing a Scott set.Alex M. McAllister - 2001 - Archive for Mathematical Logic 40 (3):147-165.
A maximal bounded forcing axiom.David Asperó - 2002 - Journal of Symbolic Logic 67 (1):130-142.
Forcing properties of ideals of closed sets.Marcin Sabok & Jindřich Zapletal - 2011 - Journal of Symbolic Logic 76 (3):1075 - 1095.
A base-matrix lemma for sets of rationals modulo nowhere dense sets.Jörg Brendle & Diana Carolina Montoya - 2012 - Archive for Mathematical Logic 51 (3-4):305-317.
Projective absoluteness for Sacks forcing.Daisuke Ikegami - 2009 - Archive for Mathematical Logic 48 (7):679-690.
More on simple forcing notions and forcings with ideals.M. Gitik & S. Shelah - 1993 - Annals of Pure and Applied Logic 59 (3):219-238.
Ultrafilters of Character $omega_1$.Klaas Pieter Hart - 1989 - Journal of Symbolic Logic 54 (1):1-15.
Mathias absoluteness and the Ramsey property.Lorenz Halbeisen & Haim Judah - 1996 - Journal of Symbolic Logic 61 (1):177-194.
Forcing with Non-wellfounded Models.Paul Corazza - 2007 - Australasian Journal of Logic 5:20-57.
Models of arithmetic and upper Bounds for arithmetic sets.Alistair H. Lachlan & Robert I. Soare - 1994 - Journal of Symbolic Logic 59 (3):977-983.
σ-Continuity and related forcings.Marcin Sabok - 2009 - Archive for Mathematical Logic 48 (5):449-464.
Cover schemes, frame-valued sets and their potential uses in spacetime physics.John Bell - manuscript

Analytics

Added to PP
2017-04-29

Downloads
27 (#607,381)

6 months
9 (#354,585)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Coherent adequate forcing and preserving CH.John Krueger & Miguel Angel Mota - 2015 - Journal of Mathematical Logic 15 (2):1550005.
Adding a club with finite conditions, Part II.John Krueger - 2015 - Archive for Mathematical Logic 54 (1-2):161-172.
Compactness versus hugeness at successor cardinals.Sean Cox & Monroe Eskew - 2022 - Journal of Mathematical Logic 23 (1).
Strongly adequate sets and adding a club with finite conditions.John Krueger - 2014 - Archive for Mathematical Logic 53 (1-2):119-136.
The approachability ideal without a maximal set.John Krueger - 2019 - Annals of Pure and Applied Logic 170 (3):297-382.

View all 7 citations / Add more citations

References found in this work

Forcing with Sequences of Models of Two Types.Itay Neeman - 2014 - Notre Dame Journal of Formal Logic 55 (2):265-298.
Coherent adequate forcing and preserving CH.John Krueger & Miguel Angel Mota - 2015 - Journal of Mathematical Logic 15 (2):1550005.
Adding a club with finite conditions, Part II.John Krueger - 2015 - Archive for Mathematical Logic 54 (1-2):161-172.
Adding Closed Unbounded Subsets of ω₂ with Finite Forcing.William J. Mitchell - 2005 - Notre Dame Journal of Formal Logic 46 (3):357-371.
Forcing with finite conditions.Gregor Dolinar & Mirna Džamonja - 2013 - Annals of Pure and Applied Logic 164 (1):49-64.

View all 6 references / Add more references