MHB Easy question regarding symbols in discrete mathematics

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The set of symbols that constitute strings in discrete mathematics is denoted by the symbol Σ, representing the alphabet. In contrast, Σ* denotes the set of all finite strings that can be formed from the symbols in Σ, including the empty string. The Kleene Star (*) indicates that the strings can consist of zero or more symbols. Therefore, Σ refers to the basic set of symbols, while Σ* encompasses all possible combinations of those symbols. Understanding this distinction is fundamental in the study of formal languages and automata theory.
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is the set of symbols that make up strings denoted by the symbol Σ or Σ* , also what is this difference?
 
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Usually the set of symbols, or the alphabet, is denoted by $\Sigma$. Then $\Sigma^*$ denotes the set of all finite strings in the alphabet $\Sigma$.
 
The star (*) is the so called Kleene Star.
It means zero-or-more.

So indeed, Σ is the alphabet, while Σ* is the set of strings consisting of zero or more symbols from the alphabet.
 

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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