Mitchell-style forcing, with small working parts and collections of\n models as side conditions, and gap-one simplified morasses

2014/11/22 by Charles G. Morgan, Charles Morgan, Morgan, Charles
Computer Science · Mathematics · #03E05 #03E35 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge

paper · pdf · doi:10.48550/arxiv.1411.6129

openalex publication_date 2014/11/22 · openalex created_date 2022/09/15 · openalex updated_date 2026/07/28

Abstract

We give a modification of Mitchell's technique for adding objects of size\n\ω₂ with conditions with finite working parts in which the collections\nof models used as side conditions are very highly structured, arguably making\nthem more wieldy. We use one such forcing (essentially a `pure side conditions'\nforcing) to answer affirmatively the question, asked independently by Shelah\nand Velleman in the late 1980s, as to whether a (\κ⁺,1)-simplified\nmorass can be added by a forcing with working parts of size <\κ.\n

Citations

• The last forcing standing with diamonds

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