Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N# define the concept of a logic frame , which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive logic frame is called complete (recursively compact , ℵ0-compact ), if every finite (respectively: recursive, countable) consistent theory has a model.  show that for logic frames built from the cardinality quantifiers “there exists at least λ ” completeness always implies .0-compactness. On the other hand  show that a recursively compact logic frame need not be ℵ0-compact. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, inheim)
['Saharon Shelah', 'Jouko Väänänen']
I am writing a research paper on a idea Recursive logic frames
[{"from": "human", "value": "I am writing a research paper on a idea Recursive logic frames"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N# define the concept of a logic frame , which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive logic frame is called complete (recursively compact , \u21350-compact ), if every finite (respectively: recursive, countable) consistent theory has a model.  show that for logic frames built from the cardinality quantifiers \u201cthere exists at least \u03bb \u201d completeness always implies .0-compactness. On the other hand  show that a recursively compact logic frame need not be \u21350-compact. (\u00a9 2006 WILEY-VCH Verlag GmbH & Co. KGaA, inheim)"}]