Journal ArticleDOI
Closed Maximality Principles and Generalized Baire Spaces
TLDR
This paper presents other canonical extensions of ZFC that provide a strong structure theory for these classes and reveals variations of the Maximality Principle introduced by Stavi and Väänänen and later rediscovered by Hamkins.Abstract:
Given an uncountable regular cardinal κ, we study the structural properties of the class of all sets of functions from κ to κ that are definable over the structure 〈H(κ+),∈〉 by a Σ1-formula with parameters. It is well known that many important statements about these classes are not decided by the axioms of ZFC together with large cardinal axioms. In this paper, we present other canonical extensions of ZFC that provide a strong structure theory for these classes. These axioms are variations of the Maximality Principle introduced by Stavi and Vaananen and later rediscovered by Hamkins.read more
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Models and games
TL;DR: Cellular Automata Machines: A New Environment for Modeling, by Tommaso Toffoli and Norman Margolus.
Journal ArticleDOI
Kurepa trees and spectra of $${\mathcal {L}}_{\omega _1,\omega }$$ L ω 1 , ω -sentences
Dima Sinapova,Ioannis Souldatos +1 more
TL;DR: A single set-theoretic tool is constructed that codes Kurepa trees to prove the following statements:
Posted Content
Forcing axioms and the complexity of non-stationary ideals
TL;DR: In this paper, the authors studied the influence of strong forcing axioms on the complexity of the non-stationary ideal on the ordinals of countable cofinality.
Journal ArticleDOI
Forcing axioms and the complexity of non-stationary ideals
TL;DR: In this article , the authors studied the influence of strong forcing axioms on the complexity of the non-stationary ideal on $$\omega _2$$ and its restrictions to certain cofinalities.
References
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Book
Classical descriptive set theory
TL;DR: In this article, the authors present a largely balanced approach, which combines many elements of the different traditions of the subject, and includes a wide variety of examples, exercises, and applications, in order to illustrate the general concepts and results of the theory.
Book ChapterDOI
Ideals and Generic Elementary Embeddings
TL;DR: The technique of generic elementary embeddings as discussed by the authors is closely analogous to conventional large cardinal embedding, the difference being that they are definable in forcing extensions of V rather than in V itself.
Journal ArticleDOI
A weak generalization of MA to higher cardinals
TL;DR: In this article, the authors generalized MA to ℵ1-complete forcing by strengthening the ℴ2-C.C. condition, which occurs in many proofs.