Intro to Metamathematics Kleene $S54$ Lemma IId Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Formalizing metamathematicsSeparation of mathematics and metamathematicsIntuitonism and metamathematics.Are there any theories that deny the continuum hypothesis that are used outside metamathematics?Metamathematics of the Banach space consequences of the Baire category theoremWhat impact would a proof that ZFC is inconsistent have on metamathematics?Why can we use induction when studying metamathematics?Beth's theorem through Robinson LemmaMetamathematics and the foundations of mathematicsDefinitions in metamathematics
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Intro to Metamathematics Kleene $S54$ Lemma IId
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Formalizing metamathematicsSeparation of mathematics and metamathematicsIntuitonism and metamathematics.Are there any theories that deny the continuum hypothesis that are used outside metamathematics?Metamathematics of the Banach space consequences of the Baire category theoremWhat impact would a proof that ZFC is inconsistent have on metamathematics?Why can we use induction when studying metamathematics?Beth's theorem through Robinson LemmaMetamathematics and the foundations of mathematicsDefinitions in metamathematics
$begingroup$
In this section, Kleene builds a formal system for primitive recursive functions. The beginning of the proof for lemma IId is skipped because it comes for general properties, but I must be missing something.
We easily see, by general properties of $vdash$, that $E^psi_1...psi_l_f_1...f_l,E_l+1...E_kvdash f_i($x$_1,...,$x$_n_i) = $ x, if
$f_i($x$_1,...,$x$_n_i) = $ x $in E^phi_i_f_i$
What is the justification in this?
(Sorry, I couldn't put more background information this is lemma four of five lemmas. It would be too much to describe in one question, so just refer to the text. Thanks)
recursive-algorithms meta-math formal-systems
asked Apr 1 at 3:41
BENGBENG
425
$endgroup$
add a comment |
$begingroup$
In this section, Kleene builds a formal system for primitive recursive functions. The beginning of the proof for lemma IId is skipped because it comes for general properties, but I must be missing something.
We easily see, by general properties of $vdash$, that $E^psi_1...psi_l_f_1...f_l,E_l+1...E_kvdash f_i($x$_1,...,$x$_n_i) = $ x, if
$f_i($x$_1,...,$x$_n_i) = $ x $in E^phi_i_f_i$
What is the justification in this?
(Sorry, I couldn't put more background information this is lemma four of five lemmas. It would be too much to describe in one question, so just refer to the text. Thanks)
recursive-algorithms meta-math formal-systems
asked Apr 1 at 3:41
BENGBENG
425
$endgroup$
add a comment |
$begingroup$
In this section, Kleene builds a formal system for primitive recursive functions. The beginning of the proof for lemma IId is skipped because it comes for general properties, but I must be missing something.
We easily see, by general properties of $vdash$, that $E^psi_1...psi_l_f_1...f_l,E_l+1...E_kvdash f_i($x$_1,...,$x$_n_i) = $ x, if
$f_i($x$_1,...,$x$_n_i) = $ x $in E^phi_i_f_i$
What is the justification in this?
(Sorry, I couldn't put more background information this is lemma four of five lemmas. It would be too much to describe in one question, so just refer to the text. Thanks)
recursive-algorithms meta-math formal-systems
asked Apr 1 at 3:41
BENGBENG
425
$endgroup$
In this section, Kleene builds a formal system for primitive recursive functions. The beginning of the proof for lemma IId is skipped because it comes for general properties, but I must be missing something.
We easily see, by general properties of $vdash$, that $E^psi_1...psi_l_f_1...f_l,E_l+1...E_kvdash f_i($x$_1,...,$x$_n_i) = $ x, if
$f_i($x$_1,...,$x$_n_i) = $ x $in E^phi_i_f_i$
What is the justification in this?
(Sorry, I couldn't put more background information this is lemma four of five lemmas. It would be too much to describe in one question, so just refer to the text. Thanks)
recursive-algorithms meta-math formal-systems
recursive-algorithms meta-math formal-systems
asked Apr 1 at 3:41
BENGBENG
425
asked Apr 1 at 3:41
BENGBENG
425
edited Apr 1 at 8:04
BENG
asked Apr 1 at 3:41
BENGBENG
425
asked Apr 1 at 3:41
BENGBENG
425
asked Apr 1 at 3:41
BENGBENG
425
425
add a comment |
add a comment |
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