Results 161 to 170 of about 377 (170)

A consequence of the Proper Forcing Axiom in topology

Publicationes Mathematicae Debrecen, 2004
Summary: If \(\langle L, < \rangle\) is a dense linear order without end-points and if \(A_1, A_2 \subset\) \(L\) are disjoint dense subsets of \(L\), then \({\mathcal O}_{A_1 A_2}\) denotes the topology on \(L\) generated by the closed intervals \([a_1,a_2]\), where \(a_1\in A_1\) and \(a_2\in A_2\).
Kurilić, M. S., Pavlović, A.
openaire   +2 more sources

8. Proper forcing axiom and partitions.

, 1989
Stevo Todorčević
openaire   +2 more sources

The $κ$-Strongly Proper Forcing Axiom

2019
We study methods to obtain the consistency of forcing axioms, and particularly higher forcing axioms. We first force over a model with a supercompact cardinal $θ>κ$ to get the consistency of the forcing axiom for $κ$-strongly proper forcing notions which are also $κ$-lattice, and then eliminate the need for large cardinals.
Asperó, David, Cox, Sean, Karagila, Asaf, Weiss, Christoph   +3 more
openaire   +1 more source

The proper forcing axiom for ℵ1-sized posets, ω1-linked symmetrically proper forcing, and the size of the continuum

Journal of Mathematical Logic
In this paper, we show that the Proper Forcing Axiom for forcing notions of size [Formula: see text] is consistent with the continuum being arbitrarily large. In fact, assuming [Formula: see text] holds and [Formula: see text] is a regular cardinal, we prove that there is a proper and [Formula: see text]-c.c.
David Asperó, Mohammad Golshani
openaire   +1 more source

Forcing the Mapping Reflection Principle by finite approximations

Archive for Mathematical Logic, 2021
Teruyuki Yorioka
exaly  

The Bounded Axiom A Forcing Axiom

Mathematical Logic Quarterly, 2010
Thilo Weinert
exaly  

Forcing with Sequences of Models of Two Types

Notre Dame Journal of Formal Logic, 2014
Itay Neeman
exaly  

Forcing axioms and the continuum hypothesis. Part II: transcending ω1-sequences of real numbers

Acta Mathematica, 2013
Justin Tatch Moore
exaly  

Bounded forcing axioms as principles of generic absoluteness

Archive for Mathematical Logic, 2000
Joan Bagaria
exaly  

Consistency strength lower bounds for the proper forcing axiom via the core model induction

Bulletin of Symbolic Logic, 2020
openaire   +1 more source