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A Model in Which Well-Orderings of the Reals Appear at a Given Projective Level
Axioms, 2022 The problem of the existence of analytically definable well-orderings at a given level of the projective hierarchy is considered. This problem is important as a part of the general problem of the study of the projective hierarchy in the ongoing ...
Vladimir Kanovei, Vassily Lyubetsky
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A Model in Which Well-Orderings of the Reals First Appear at a Given Projective Level, Part II
Mathematics, 2023 We consider the problem of the existence of well-orderings of the reals, definable at a certain level of the projective hierarchy. This research is motivated by the modern development of descriptive set theory.
Vladimir Kanovei, Vassily Lyubetsky
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Mathematics, 2023 A model of set theory ZFC is defined in our recent research, in which, for a given n≥3, (An) there exists a good lightface Δn1 well-ordering of the reals, but (Bn) no well-orderings of the reals (not necessarily good) exist in the previous class Δn−11 ...
Vladimir Kanovei, Vassily Lyubetsky
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Projective well orders and coanalytic witnesses
Annals of Pure and Applied Logic, 2022 19 ...
Jeffrey Bergfalk +2 more
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Mathematics, 2023 We make use of generalized iterations of the Sacks forcing to define cardinal-preserving generic extensions of the constructible universe L in which the axioms of ZF hold and in addition either (1) the parameter-free countable axiom of choice ACω* fails,
Vladimir Kanovei, Vassily Lyubetsky
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Cofinitary groups and projective well-orders
, 2023 21 pages ...
Fischer, Vera +2 more
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A computability theoretic equivalent to Vaught's conjecture [PDF]
, 2013 We prove that, for every theory $T$ which is given by an ${\mathcal L}_{\omega_1,\omega}$ sentence, $T$ has less than $2^{\aleph_0}$ many countable models if and only if we have that, for every $X\in 2^\omega$ on a cone of Turing degrees, every $X ...
Montalban, Antonio
core +1 more source
The Complexity of Simultaneous Geometric Graph Embedding [PDF]
, 2015 Given a collection of planar graphs $G_1,\dots,G_k$ on the same set $V$ of $n$ vertices, the simultaneous geometric embedding (with mapping) problem, or simply $k$-SGE, is to find a set $P$ of $n$ points in the plane and a bijection $\phi: V \to P$ such ...
Cardinal, Jean, Kusters, Vincent
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BPFA and projective well-orderings of the reals
The Journal of Symbolic Logic, 2011 AbstractIf the bounded proper forcing axiom BPFA holds and ω1 = ω1L, then there is a lightface Σ31 well-ordering of the reals. The argument combines a well-ordering due to Caicedo-Veličković with an absoluteness result for models of MA in the spirit of “David's trick.” We also present a general coding scheme that allows us to show that BPFA is ...
Caicedo, Andrés Eduardo +1 more
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Measure, category and projective wellorders
Journal of Logic and Analysis, 2015 Summary: We show that each admissible assignment of \(\aleph_1\) and \(\aleph_2\) to the cardinal invariants in the Cichoń Diagram is consistent with the existence of a projective wellorder of the reals.
Fischer, Vera +2 more
openaire +5 more sources