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Forcing with Invariant Measures

delete2025-11-01
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OA
AI
N
Nathanael Ackerman
C
Cameron E. Freer
M
Mohammad Golshani
M
Mostafa Mirabi *
R
Rehana Patel
DOI：10.1007/s11787-025-00394-2delete
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摘要

摘要

En 中文
本文介绍了一种模型论的泛化概念，即通过随机实数进行的力迫，其中力迫产生随机泛结构。具体而言，我们考虑在具有（可能不可数的）无限集X的L-结构的空间上，具有κ-博雷尔概率测度的力迫，重点研究那些在Sym(X)作用下的不变测度。我们证明了当X可数时，任何Sym(X)-不变测度可以唯一扩展为Sym(Y)-不变测度（其中Y不可数），并证明使用此类测度的力迫满足可数链条件。我们还展示了可以统一区分这些随机泛结构与来自强Fraïssé类的力迫所产生的Cohen泛结构：存在一个低复杂度的κ-博雷尔集，包含所有非高度齐性的Cohen泛结构，但不包含任何随机泛结构，这意味着非高度齐性的结构不能同时是Cohen泛结构和随机泛结构。最后，我们回答了Kostana在ω₁情况下提出的公开问题，通过建立强Fraïssé类力迫与Cohen力迫之间的联系。
Keyword:
Fra & iuml
ss & eacute
limit
random forcing
Cohen forcing
generic structures
invariant measures
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期刊

L
Logica Universalis
IF:
0.5
论文数:
25
被引数:
0

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Wesleyan University
学者数:
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I
institute for research in fundamental sciences ipm
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Harvard University
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被引数: 28.7W
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引用论文

引用论文

Completing theories by forcing
errAnnals of Mathematical Logic
IF0
err1970-10-01
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errBarwise,Jon; Robinson,Abraham
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Cohen-like first order structures
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errKostana,Ziemowit
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Relativized Grothendieck topoi
errAnnals of Pure and Applied Logic
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errAckerman,Nathanael Leedom
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Transitivity of permutation groups on unordered sets
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A Model of Set-Theory in Which Every Set of Reals is Lebesgue Measurable
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On sets of integers containing k elements in arithmetic progression
errActa Arithmetica
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errE. Szemerédi
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Forcing, Arithmetic, Division Rings
errLecture Notes in Mathematics
IF0
err1975-01-01
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errHirschfeld,Joram; Wheeler,William H.
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Model Theory
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errIsrael Journal of Mathematics
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errHaim Gaifman
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Abraham Robinson. Forcing in model theory. Symposia mathematica, vol. 5, Istituto Nazionale di Alta Matematica, Academic Press, London and New York 1971, pp. 69–82. - Jon Barwise and Abraham Robinson. Completing theories by forcing. Annals of mathematical logic, vol. 2 no. 2 (1970), pp. 119–142. - Abraham Robinson. Infinite forcing in model theory. Proceedings of the Second Scandinavian Logic Symposium, edited by J. E. Fenstad, Studies in logic and the foundations of mathematics, vol. 63, North-Holland Publishing Company, Amsterdam and London 1971, pp. 317–340. - Abraham Robinson. Forcing in model theory. Actes du Congrès International des Mathematiciens 1970, Gauthier-Villars, Paris 1971, Vol. 1, pp. 245–250.
errJournal of Symbolic Logic
IF0
err1975-12-01
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PREAI
errKeisler,H. Jerome
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