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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
doaj   +2 more sources

A Model in Which Well-Orderings of the Reals First Appear at a Given Projective Level, Part III—The Case of Second-Order PA

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
doaj   +2 more sources

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
doaj   +2 more sources

Projective well orders and coanalytic witnesses

Annals of Pure and Applied Logic, 2022
19 ...
Jeffrey Bergfalk, Vera Fischer, Corey Bacal Switzer   +2 more
openaire   +2 more sources

On the Significance of Parameters in the Choice and Collection Schemata in the 2nd Order Peano Arithmetic

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
doaj   +1 more source

Cofinitary groups and projective well-orders

, 2023
21 pages ...
Fischer, Vera, Schembecker, Lukas, Schrittesser, David   +2 more
openaire   +2 more sources

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, Friedman, Sy-David   +1 more
openaire   +4 more sources

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, Friedman, Sy, Khomskii, Yurii   +2 more
openaire   +5 more sources

Cardinal characteristics and projective wellorders

Annals of Pure and Applied Logic, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fischer, Vera, Friedman, Sy-David
openaire   +2 more sources

Jensen ${\Delta }_n^1$ Reals by Means of ZFC and Second-Order Peano Arithmetic

Axioms
It was established by Jensen in 1970 that there is a generic extension L[a] of the constructible universe L by a non-constructible real a∉L, minimal over L, such that a is Δ31 in L[a].
Vladimir Kanovei, Vassily Lyubetsky
doaj   +1 more source