Projective well-orderings - Open Access .click

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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 A. Lyubetsky
exaly +3 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 A. Lyubetsky
exaly +3 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 A. Lyubetsky
exaly +3 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

Jensen $Δ_{n}^{1}$ 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

CP² skyrmions and skyrmion crystals in realistic quantum magnets. [PDF]

Nat Commun, 2023
Zhang H +4 more
europepmc +1 more source

Entanglement of Signal Paths via Noisy Superconducting Quantum Devices. [PDF]

Entropy (Basel), 2023
Shi W, Malaney R.
europepmc +1 more source

Experimental demonstration of continuous quantum error correction. [PDF]

Nat Commun, 2022
Livingston WP +5 more
europepmc +1 more source

A model of <i>d</i>-wave superconductivity, antiferromagnetism, and charge order on the square lattice. [PDF]

Proc Natl Acad Sci U S A, 2023
Christos M +5 more
europepmc +1 more source

Modern perspectives in Proof Theory. [PDF]

Philos Trans A Math Phys Eng Sci, 2023
Aguilera JP, Pakhomov F, Weiermann A.
europepmc +1 more source

forcing
projective classes