强迫公理和非定常理想的复杂性。

IF 0.8 4区数学 Q2 MATHEMATICS

Monatshefte fur Mathematik Pub Date : 2022-01-01 Epub Date: 2022-06-27 DOI:10.1007/s00605-022-01734-w

Sean Cox, Philipp Lücke

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引用次数: 0

摘要

研究了强强迫公理对ω 2上非平稳理想的复杂性的影响及其对某些伴随性的限制。我们的主要结果表明，马丁极大值的增强并不能决定ω 2上的非平稳理想对可数共度序数集的约束是否为Δ 1 -可由H (ω 3)中的参数公式定义。在证明这一结果中发展的技术也使我们能够证明与CH兼容的ω 2上的完全非平稳理想和强强迫公理的类似结果。最后，我们回答了S. Friedman, Wu和zdomsky的一个问题，证明了ω 2上的非平稳理想的Δ 1 -可定义性与ω 2上任意大的连续统函数相容。

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Forcing axioms and the complexity of non-stationary ideals.

We study the influence of strong forcing axioms on the complexity of the non-stationary ideal on $ω_{2}$ and its restrictions to certain cofinalities. Our main result shows that the strengthening ${MM}^{+ +}$ of Martin's Maximum does not decide whether the restriction of the non-stationary ideal on $ω_{2}$ to sets of ordinals of countable cofinality is $Δ_{1}$ -definable by formulas with parameters in $H (ω_{3})$ . The techniques developed in the proof of this result also allow us to prove analogous results for the full non-stationary ideal on $ω_{2}$ and strong forcing axioms that are compatible with $CH$ . Finally, we answer a question of S. Friedman, Wu and Zdomskyy by showing that the $Δ_{1}$ -definability of the non-stationary ideal on $ω_{2}$ is compatible with arbitrary large values of the continuum function at $ω_{2}$ .

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来源期刊

Monatshefte fur Mathematik 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

155

审稿时长

4-8 weeks

期刊介绍： The journal was founded in 1890 by G. v. Escherich and E. Weyr as "Monatshefte für Mathematik und Physik" and appeared with this title until 1944. Continued from 1948 on as "Monatshefte für Mathematik", its managing editors were L. Gegenbauer, F. Mertens, W. Wirtinger, H. Hahn, Ph. Furtwängler, J. Radon, K. Mayrhofer, N. Hofreiter, H. Reiter, K. Sigmund, J. Cigler. The journal is devoted to research in mathematics in its broadest sense. Over the years, it has attracted a remarkable cast of authors, ranging from G. Peano, and A. Tauber to P. Erdös and B. L. van der Waerden. The volumes of the Monatshefte contain historical achievements in analysis (L. Bieberbach, H. Hahn, E. Helly, R. Nevanlinna, J. Radon, F. Riesz, W. Wirtinger), topology (K. Menger, K. Kuratowski, L. Vietoris, K. Reidemeister), and number theory (F. Mertens, Ph. Furtwängler, E. Hlawka, E. Landau). It also published landmark contributions by physicists such as M. Planck and W. Heisenberg and by philosophers such as R. Carnap and F. Waismann. In particular, the journal played a seminal role in analyzing the foundations of mathematics (L. E. J. Brouwer, A. Tarski and K. Gödel). The journal publishes research papers of general interest in all areas of mathematics. Surveys of significant developments in the fields of pure and applied mathematics and mathematical physics may be occasionally included.