What is the theory without power set?

DOI10.1002/malq.201500019zbMath1375.03059arXiv1110.2430OpenAlexW1933515991MaRDI QIDQ2827952

Joel David Hamkins, Thomas A. Johnstone, Victoria Gitman

Publication date: 24 October 2016

Published in: Mathematical Logic Quarterly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.2430

zbMATH Keywords

forcingpower set axiomtheory of ultrapowers

Mathematics Subject Classification ID

Consistency and independence results (03E35) Axiomatics of classical set theory and its fragments (03E30)

Related Items (29)

Indestructibility properties of Ramsey and Ramsey-like cardinals ⋮ TAKING REINHARDT’S POWER AWAY ⋮ Generalized Effective Reducibility ⋮ THE Σ₁-DEFINABLE UNIVERSAL FINITE SEQUENCE ⋮ On extendible cardinals and the GCH ⋮ Strongly uplifting cardinals and the boldface resurrection axioms ⋮ Forcing a set model of Z3 + Harrington's Principle ⋮ The strong reflecting property and Harrington's Principle ⋮ Open determinacy for class games ⋮ Inner models with large cardinal features usually obtained by forcing ⋮ A good lightface \(\varDelta_n^1\) well-ordering of the reals does not imply the existence of boldface \(\mathbf{\Delta}_{n - 1}^1\) well-orderings ⋮ All melodies are lost -- recognizability for weak and strong \(\alpha \)-register machines ⋮ Comparing material and structural set theories ⋮ The distribution of ITRM-recognizable reals ⋮ The least weakly compact cardinal can be unfoldable, weakly measurable and nearly \(\theta\)-supercompact ⋮ Hyperclass Forcing in Morse-Kelley Class Theory ⋮ Elementary epimorphisms between models of set theory ⋮ BI-INTERPRETATION IN WEAK SET THEORIES ⋮ Definable Hamel bases and ${\sf AC}_\omega ({\mathbb R})$ ⋮ Kelley–Morse set theory does not prove the class Fodor principle ⋮ Generalizations of the Kunen inconsistency ⋮ Set-theoretic blockchains ⋮ The weakly compact reflection principle need not imply a high order of weak compactness ⋮ Torsion-free abelian groups are consistently $ {\rm a}\Delta ^1_2$-complete ⋮ A model of second-order arithmetic satisfying AC but not DC ⋮ Projective Measure Without Projective Baire ⋮ Lower bounds on \(\beta (\alpha)\) ⋮ Easton's theorem for Ramsey and strongly Ramsey cardinals ⋮ INITIAL SELF-EMBEDDINGS OF MODELS OF SET THEORY

Cites Work

• Unnamed Item
• Indestructible strong unfoldability
• Certain very large cardinals are not created in small forcing extensions
• A model of set-theory in which every set of reals is Lebesgue measurable
• Ramsey-like cardinals
• Proper Forcing
• Determinacy in L(ℝ)
• Canonical seeds and Prikry trees
• Extensions with the approximation and cover properties have no new large cardinals
• The interdependence of certain consequences of the axiom of choice

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