A model of second-order arithmetic satisfying AC but not DC
SD Friedman, V Gitman, V Kanovei - Journal of Mathematical Logic, 2019 - World Scientific
We show that there is a β-model of second-order arithmetic in which the choice scheme
holds, but the dependent choice scheme fails for a Π 2 1-assertion, confirming a conjecture …
holds, but the dependent choice scheme fails for a Π 2 1-assertion, confirming a conjecture …
Sacks forcing, Laver forcing, and Martin's axiom
H Judah, AW Miller, S Shelah - Archive for Mathematical Logic, 1992 - Springer
In this paper we study the question assuming MA+⌝ CH does Sacks forcing or Laver forcing
collapse cardinals? We show that this question is equivalent to the question of what is the …
collapse cardinals? We show that this question is equivalent to the question of what is the …
On the significance of parameters and the projective level in the Choice and Comprehension axioms
We make use of generalized iterations of Jensen forcing to define a cardinal-preserving
generic model of ZF for any $ n\ge 1$ and each of the following four Choice hypotheses:(1) …
generic model of ZF for any $ n\ge 1$ and each of the following four Choice hypotheses:(1) …
On Sacks forcing and the Sacks property
S Geschke, S Quickert - Classical and New Paradigms of Computation and …, 2004 - Springer
In this survey we explain the general idea of forcing, present Sacks forcing with some of its
properties, give an overview of closely related forcing notions, and investigate the influence …
properties, give an overview of closely related forcing notions, and investigate the influence …
[HTML][HTML] Counterexamples to countable-section Π21 uniformization and Π31 separation
Counterexamples to countable-section Π21 uniformization and Π31 separation - ScienceDirect
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Definable minimal collapse functions at arbitrary projective levels
Using a nonLaver modification of Uri Abraham's minimal 1 3 collapse function, we define a
generic extension L [a] by a real a, in which, for a given n≥ 3,{a} is a lightface 1 n singleton …
generic extension L [a] by a real a, in which, for a given n≥ 3,{a} is a lightface 1 n singleton …
[PDF][PDF] Jensen forcing at an inaccessible and a model of Kelley-Morse satisfying CC but not DCω
SD Friedman, V Gitman - 2024 - victoriagitman.github.io
Jensen used♦ to construct a forcing notion J of perfect trees which has the ccc and adds a
unique generic real. Given an inaccessible κ, we generalize Jensen's construction, using♦ …
unique generic real. Given an inaccessible κ, we generalize Jensen's construction, using♦ …
[PDF][PDF] Sacks forcing collapses to
P Simon - Commentationes Mathematicae Universitatis Carolinae, 1993 - dml.cz
Commentationes Mathematicae Universitatis Carolinae Page 1 Commentationes
Mathematicae Universitatis Carolinae Petr Simon Sacks forcing collapses c to b …
Mathematicae Universitatis Carolinae Petr Simon Sacks forcing collapses c to b …
A good lightface Δn1 well-ordering of the reals does not imply the existence of boldface Δn− 11 well-orderings
We make use of a finite support product of the Jensen-type forcing notions to define a model
of the set theory ZFC in which, for a given n≥ 3, there exists a good lightface Δ n 1 well …
of the set theory ZFC in which, for a given n≥ 3, there exists a good lightface Δ n 1 well …
[PDF][PDF] CCC posets of perfect trees
B Velickovic - Compositio Mathematica, 1991 - numdam.org
CCC posets of perfect trees Page 1 COMPOSITIO MATHEMATICA BOBAN VELICKOVIC
CCC posets of perfect trees Compositio Mathematica, tome 79, no 3 (1991), p. 279-294 <http://www.numdam.org/item?id=CM_1991__79_3_279_0> …
CCC posets of perfect trees Compositio Mathematica, tome 79, no 3 (1991), p. 279-294 <http://www.numdam.org/item?id=CM_1991__79_3_279_0> …