Patterns of resemblance: Difference between revisions
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==Stability== |
==Stability== |
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It has been known since (Carlson 2001) that certain variants of patterns of resemblance involving stability result in a core isomorphic to that of the usual patterns of resemblance. In particular, if \(\alpha\preceq\beta\) is interpreted as \(L_\alpha\prec_{\Sigma_1}L_\beta\), then the core of \((\textrm{Ord},0,+,\leq,\preceq)\) is isomorphic to the core of additive first-order patterns,<ref name="ElementaryPatterns" /><sup>p.20</sup> so it has order type \(\psi_0(\Omega_\omega)\). This may be seen as somewhat similar to the connection between BMS and stability used in Yto's termination proof for BMS. |
It has been known since (Carlson 2001) that certain variants of patterns of resemblance involving stability result in a core isomorphic to that of the usual patterns of resemblance. In particular, if \(\alpha\preceq\beta\) is interpreted as \(L_\alpha\prec_{\Sigma_1}L_\beta\), then the core of \((\textrm{Ord},0,+,\leq,\preceq)\) is isomorphic to the core of additive first-order patterns,<ref name="ElementaryPatterns" /><sup>p.20</sup> so it has order type \(\psi_0(\Omega_\omega)\). This may be seen as somewhat similar to the connection between BMS and stability used in Yto's termination proof for BMS. |
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==Citations== |
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