Search Results - "JOHNSTONE, Thomas A"

Resurrection axioms and uplifting cardinals by Hamkins, Joel David, Johnstone, Thomas A.

“…We introduce the resurrection axioms, a new class of forcing axioms, and the uplifting cardinals, a new large cardinal notion, and prove that various instances…”
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Strongly unfoldable cardinals made indestructible by Johnstone, Thomas A.

“…I provide indestructibility results for large cardinals consistent with V = L, such as weakly compact, indescribable and strongly unfoldable cardinals. The…”
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What is the theory without power set? by Gitman, Victoria, Hamkins, Joel David, Johnstone, Thomas A.

“…We show that the theory , consisting of the usual axioms of but with the power set axiom removed—specifically axiomatized by extensionality, foundation,…”
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THE PROPER AND SEMI-PROPER FORCING AXIOMS FOR FORCING NOTIONS THAT PRESERVE N2 OR N3 by HAMKINS, Joel David, JOHNSTONE, Thomas A, KNIGHT, Julia

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Indestructibility properties of Ramsey and Ramsey-like cardinals by Gitman, Victoria, Johnstone, Thomas A.

“…We develop new techniques, for use in indestructibility arguments, of lifting embeddings on transitive set models of ZFC− which lack closure and of lifting…”
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Strongly uplifting cardinals and the boldface resurrection axioms by Hamkins, Joel David, Johnstone, Thomas A.

“…We introduce the strongly uplifting cardinals, which are equivalently characterized, we prove, as the superstrongly unfoldable cardinals and also as the…”
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What is the theory ZFC without power set? by Gitman, Victoria, Hamkins, Joel David, Johnstone, Thomas A.

“…We show that the theory ZFC-, consisting of the usual axioms of ZFC but with the power set axiom removed—specifically axiomatized by extensionality,…”
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What is the theory without power set? V. Gitman, J. D. Hamkins, and T. A. Johnstone What is the theory ZFC without power set? by Gitman, Victoria, Hamkins, Joel David, Johnstone, Thomas A

“…We show that the theory ZFC -, consisting of the usual axioms of ZFC but with the power set axiom removed--specifically axiomatized by extensionality,…”
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The Proper and Semi-Proper Forcing Axioms for Forcing Notions That Preserve ℵ₂ or ℵ by Hamkins, Joel David, Johnstone, Thomas A.

“…We prove that the PFA lottery preparation of a strongly unfoldable cardinal κ under $\neg 0^{♯}$ forces PFA(ℵ₂-preserving), PFA(ℵ₃-preserving) and…”
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On ground model definability by Gitman, Victoria, Johnstone, Thomas A

“…Laver, and Woodin independently, showed that models of ${\rm ZFC}$ are uniformly definable in their set-forcing extensions, using a ground model parameter. We…”
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Strongly unfoldable cardinals made indestructible by Johnstone, Thomas A

“…I provide indestructibility results for weakly compact, indescribable and strongly unfoldable cardinals. In order to make these large cardinals indestructible,…”
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Strongly uplifting cardinals and the boldface resurrection axioms by Hamkins, Joel David, Johnstone, Thomas A

“…We introduce the strongly uplifting cardinals, which are equivalently characterized, we prove, as the superstrongly unfoldable cardinals and also as the almost…”
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Resurrection axioms and uplifting cardinals by Hamkins, Joel David, Johnstone, Thomas A

“…We introduce the resurrection axioms, a new class of forcing axioms, and the uplifting cardinals, a new large cardinal notion, and prove that various instances…”
Get full text

The proper and semi-proper forcing axioms for forcing notions that preserve \aleph _2 or \aleph _3 by Joel David Hamkins, Thomas A. Johnstone

“…We prove that the PFA lottery preparation of a strongly unfoldable cardinal \kappa under \neg 0^\sharp forces \operatorname {PFA}(\aleph _2\text…”
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What is the theory ZFC without power set? by Gitman, Victoria, Hamkins, Joel David, Johnstone, Thomas A

“…We show that the theory ZFC-, consisting of the usual axioms of ZFC but with the power set axiom removed-specifically axiomatized by extensionality,…”
Get full text