Patterns of resemblance: Difference between revisions

Let \(a \subseteq_{fin} b\) hold iff \(a\) is a finite subset of \(b\), and use interval notation for ordinals. \(\alpha <_1 \beta\) holds iff for all \(X \subseteq_{fin} [0,\alpha)\) and \(Y \subseteq_{fin} [\alpha,\beta)\), there exists a \(\tilde Y\subseteq_{fin} [0,\alpha)\) such that \(X \cup Y \cong X \cup \tilde Y\), where \(\cong\) is isomorphism with respect to the language of first-order patterns. (I think <ref name="OrdinalArithmeticSigmaOne" /> is a citation)