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Note on Deduction Theorems in contraction‐free logics
Author(s) -
Chvalovský Karel,
Cintula Petr
Publication year - 2012
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201110065
Subject(s) - finitary , mathematics , contraction (grammar) , hierarchy , natural deduction , pure mathematics , mathematical economics , discrete mathematics , law , medicine , political science
This paper provides a finer analysis of the well‐known form of the Local Deduction Theorem in contraction‐free logics (understood as Tarski‐style finitary structural consequence relations). An infinite hierarchy of its natural strengthenings is introduced and studied. The main results are the separation of its initial four members and the subsequent collapse of the hierarchy.