101 citations
- Centre National de la Recherche ScientifiqueFR9 papers
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7 papers · 1 filter
Axiomatizing Rumsfeld Ignorance
Jie Fan
In a recent paper, Kit Fine presents some striking results concerning the logical properties of (first-order) ignorance, second-order ignorance and Rumsfeld ignorance. However, Rum…
On Erdos--Dushnik--Miller theorem without AC
Amitayu Banerjee, Alexa Gopaulsingh
In set theory without the Axiom of Choice, we study the possible placement of Erdos-Dushnik-Miller theorem restricted to an uncountable set of vertices in the hierarchy of weak cho…
Unreachability of Inductive-Like Pointclasses in
Derek Levinson, Itay Neeman, Grigor Sargsyan
Hjorth proved from that there is no sequence of distinct sets of length . Sargsyan extended Hjorth's technique to show there is no sequence of distinc…
Maximal independent sets, variants of chain/antichain principle and cofinal subsets without AC
Amitayu Banerjee
In set theory without the Axiom of Choice (AC), we observe new relations of the following statements with weak choice principles. 1. Every locally finite connected graph has a maxi…
Chromatic number of the product of graphs, graph homomorphisms, Antichains and cofinal subsets of posets without AC
Amitayu Banerjee, Zalán Gyenis
We have observations concerning the set theoretic strength of the following combinatorial statements without the axiom of choice. 1. If in a partially ordered set, all chains are f…
On The Computability of Perfect Subsets of Sets with Positive Measure
Chitat Chong, Wei Li, Wei Wang +1
A set with positive measure contains a perfect subset. We study such perfect subsets from the viewpoint of computability and prove that these sets can have weak c…