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What is Hanf Numbers and Order Properties about?

This document presents an analysis of Hanf numbers for infinitary logics. It defines several cardinal and ordinal-valued functions related to Hanf numbers, including μ*(γ,κ) which provides an upper bound on the order property for theories of size ≤ κ. Some key results are that μ*(γ,κ) is bounded above by (|γ|κ)+, and the ordinal δ*(γ,κ) bounding μ*(γ,κ) is greater than |γ|κ when κ has uncountable cofinality. The functions are used to bound values of the function μ(λ,κ) studied in a previous paper on classif

Author

HutsDM

Language

EN