MHB Logic Book: Definitions, Language & Existential Formulas

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A user seeks recommendations for a logic book that includes definitions of concepts such as language and positive existential formulas. Another participant suggests "Logic, Language, and Meaning, Volume 1: Introduction to Logic" by Gamut as a potential resource. The discussion emphasizes the need for clarity in definitions within logic studies. Participants are encouraged to share additional suggestions if they know of other relevant texts. The conversation highlights the importance of foundational knowledge in logic.
mathmari
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Hey! :o

Could you suggest a book of logic that contains definitions, like the definition of a language, of an (positive) existential formula, etc?
 
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Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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