Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  examine combinatorial aspects and consistency strength properties of almost Ramsey cardinals. Without the Axiom of Choice, successor cardinals may be almost Ramsey. From fairly mild supercompactness assumptions,  construct a model of ZF + \({\neg {\rm AC}_\omega}\) in which every infinite cardinal is almost Ramsey. Core model arguments show that strong assumptions are necessary. Without successors of singular cardinals,  can aken this to an equiconsistency of the following theories: “ZFC + There is a proper class of regular almost Ramsey cardinals”, and “ZF + DC + All infinite cardinals except possibly successors of singular cardinals are almost Ramsey”.
['Arthur W. Apter', 'Peter Koepke']
I am writing a research paper on a idea Making all cardinals almost Ramsey
[{"from": "human", "value": "I am writing a research paper on a idea Making all cardinals almost Ramsey"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  examine combinatorial aspects and consistency strength properties of almost Ramsey cardinals. Without the Axiom of Choice, successor cardinals may be almost Ramsey. From fairly mild supercompactness assumptions,  construct a model of ZF + \\({\\neg {\\rm AC}_\\omega}\\) in which every infinite cardinal is almost Ramsey. Core model arguments show that strong assumptions are necessary. Without successors of singular cardinals,  can aken this to an equiconsistency of the following theories: \u201cZFC + There is a proper class of regular almost Ramsey cardinals\u201d, and \u201cZF + DC + All infinite cardinals except possibly successors of singular cardinals are almost Ramsey\u201d."}]