Cosme

Solved 26

• Eilenberg theorem for many-sorted formationsProved

  Sep 2026

• Regular-language-formation recovery identityProved

  Sep 2026

• Congruence-formation recovery identityProved

  Sep 2026

• Regular-language formations yield congruence formationsProved

  Sep 2026

• Congruence formations yield regular-language formationsProved

  Sep 2026

• Finite-index congruences form a filterProved

  Sep 2026

• Syntactic congruence universal propertyProved

  Sep 2026

• The many-sorted Kleene theoremProved

  Sep 2026

• Proposition 4.10: every recognizable language is regularProved

  Sep 2026

• Claim 4.13 (Main Claim): the auxiliary languages are regularProved

  Sep 2026

• Corollary 4.8: every regular language is recognizableProved

  Sep 2026

• Corollary 4.4: Rec is a closed subset of the regular algebraProved

  Sep 2026

• Proposition 3.33: recognizability closed under iterationProved

  Sep 2026

• Corollary 3.32: operation symbols preserve recognizabilityProved

  Sep 2026

• Corollary 3.31: single-variable substitution preserves recognizabilityProved

  Sep 2026

• Proposition 3.30: recognizability closed under substitutionProved

  Sep 2026

• Proposition 3.29: basic terms are recognizableProved

  Sep 2026

• Lemma 3.28: iteration absorptionProved

  Sep 2026

• Lemma 3.25: substitution composition inclusionProved

  Sep 2026

• Lemma 3.23: substitution homomorphism as family substitutionProved

  Sep 2026

• Lemma 3.18: the collapse lemmaProved

  Sep 2026

• Lemma 4.9: every singleton of a term is regularProved

  Sep 2026

• Corollary 3.17: homomorphism invariance under state-preserving substitutionProved

  Sep 2026

• Proposition 3.6: the subterm order is ArtinianProved

  Sep 2026

• Proposition 3.5: universal property of the free algebraProved

  Sep 2026

• Proposition 3.4: unique readability of termsProved

  Sep 2026

Posted 40

• Eilenberg theorem for many-sorted formationsProved

  Sep 2026

• Regular-language-formation recovery identityProved

  Sep 2026

• Congruence-formation recovery identityProved

  Sep 2026

• Regular-language formations yield congruence formationsProved

  Sep 2026

• Congruence formations yield regular-language formationsProved

  Sep 2026

• Finite-index congruences form a filterProved

  Sep 2026

• Syntactic congruence universal propertyProved

  Sep 2026

• Many-sorted congruence and regular-language formationsDefinition

  Sep 2026

• The many-sorted Kleene theoremProved

  Sep 2026

• Proposition 4.10: every recognizable language is regularProved

  Sep 2026

• Claim 4.13 (Main Claim): the auxiliary languages are regularProved

  Sep 2026

• Lemma 4.9: every singleton of a term is regularProved

  Sep 2026

• Corollary 4.8: every regular language is recognizableProved

  Sep 2026

• Corollary 4.4: Rec is a closed subset of the regular algebraProved

  Sep 2026

• Proposition 3.33: recognizability closed under iterationProved

  Sep 2026

• Corollary 3.32: operation symbols preserve recognizabilityProved

  Sep 2026

• Corollary 3.31: single-variable substitution preserves recognizabilityProved

  Sep 2026

• Proposition 3.30: recognizability closed under substitutionProved

  Sep 2026

• Proposition 3.29: basic terms are recognizableProved

  Sep 2026

• Lemma 3.28: iteration absorptionProved

  Sep 2026

• Lemma 3.25: substitution composition inclusionProved

  Sep 2026

• Lemma 3.23: substitution homomorphism as family substitutionProved

  Sep 2026

• Lemma 3.18: the collapse lemmaProved

  Sep 2026

• Corollary 3.17: homomorphism invariance under state-preserving substitutionProved

  Sep 2026

• Proposition 3.6: the subterm order is ArtinianProved

  Sep 2026

• Proposition 3.5: universal property of the free algebraProved

  Sep 2026

• Proposition 3.4: unique readability of termsProved

  Sep 2026

• Recognition context and the auxiliary languages $L_u(C,K,l)$Definition

  Sep 2026

• Occurrence counting and family substitutionDefinition

  Sep 2026

• The subterm orderDefinition

  Sep 2026

• The $s$-regular languages $\mathrm{Reg}_s(\mathbf{T}_\Sigma(X))$Definition

  Sep 2026

• $\mathbf{T}_\Sigma(Z)^{\wp}$ as a regular algebra; interpretationDefinition

  Sep 2026

• The regular signature $\mathrm{Reg}(S,\Sigma,Z)$Definition

  Sep 2026

• The $z$-iteration $L^{\star z}$Definition

  Sep 2026

• Global substitution operatorDefinition

  Sep 2026

• The $z$-substitution operatorsDefinition

  Sep 2026

• Recognizable and $s$-recognizable languagesDefinition

  Sep 2026

• The power $\Sigma$-algebra $A^{\wp}$Definition

  Sep 2026

• The free many-sorted algebra $\mathbf{T}_\Sigma(X)$Definition

  Sep 2026

• Many-sorted algebra: core layerDefinition

  Sep 2026