منابع مشابه
A dedekind finite borel set
In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if B ⊆ 2 is a Gδσ-set then either B is countable or B contains a perfect subset. Second, we prove that if 2 is the countable union of countable sets, then there exists an Fσδ set C ⊆ 2 such that C is uncountable but contains no perfect subset. Finally, we c...
متن کاملSet-ΛΛαppings on Dedekind Sets
HajnaPs free set principle is equivalent to the axiom of choice, and some of its variants for Dedekind-finite sets are equivalent to countable forms of the axiom of choice. As was observed by Freiling [4] in the case of X = IR, if one applies some heuristics about selecting elements of X at random, one obtains assertions of the form "Every set-mapping/:X-> I (x£f(x)) has a nontrivial free subse...
متن کاملDedekind-finite Strongly Clean Rings
In this paper we partially answer two open questions concerning clean rings. First, we demonstrate that if a quasi-continuous module is strongly clean then it is Dedekind-finite. Second, we prove a partial converse. We also prove that all clean decompositions on submodules of continuous modules extend to the entire module.
متن کاملA Nonhereditary Borel-cover γ-set
In this paper we prove that if there is a Borel-cover γ-set of cardinality the continuum, then there is one which is not hereditary. In this paper we answer some of the questions raised by Bartoszyński and Tsaban [1] concerning hereditary properties of sets defined by certain Borel covering properties. Define. An ω-cover of a set X is a family of sets such that every finite subset of X is inclu...
متن کاملBorel stay-in-a-set games
Consider an n-person stochastic game with Borel state space S, compact metric action sets A 1 , A 2 ,. .. , A n , and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state x and continuously on the actions (a 1 , a 2 ,. .. , a n) of the players. If the payoff to each player i is 1 or 0 according to whether or not the st...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2010
ISSN: 0933-5846,1432-0665
DOI: 10.1007/s00153-010-0195-6