On conservative extensions in logics with infinitary predicates

Studia Logica 92 (1):121 - 135 (2009)
If the language is extended by new individual variables, in classical first order logic, then the deduction system obtained is a conservative extension of the original one. This fails to be true for the logics with infinitary predicates. But it is shown that restricting the commutativity of quantifiers and the equality axioms in the extended system and supposing the merry-go-round property in the original system, the foregoing extension is already conservative. It is shown that these restrictions are crucial for an extension to be conservative. The origin of the results is algebraic logic.
Keywords algebraic logic  conservative extension  infinitary predicates
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Miklós Ferenczi (2012). On Representability of Neatly Embeddable Cylindric Algebras. Journal of Applied Non-Classical Logics 10 (3-4):303-315.

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