Notations - Revision history

Lionel Vaux at 11:56, 6 September 2012

2012-09-06T11:56:39Z

2012-09-06T11:36:49Z

‎Miscellaneous

2009-10-19T08:48:19Z

‎Miscellaneous: isomorphism added

2009-10-12T20:47:46Z

‎Coherent spaces: link to the 'coherent spaces' page

2009-07-06T14:48:23Z

‎Finiteness spaces: justify the notation of fniiteness structures

2009-07-06T14:41:08Z

‎Semantics: Notations for finiteness spaces

2009-02-07T15:44:51Z

‎Coherent spaces

2009-02-07T15:19:50Z

Notations for coherent spaces

2009-01-17T16:12:19Z

‎Formulas

2009-01-10T22:30:15Z

‎Rule names: implicit R for one-sided

@@ Line 68: / Line 68: @@
 * Web of the finiteness space <math>\mathcal A</math>: <math>\web{\mathcal A}</math>
 * Finiteness structure of the space <math>\mathcal A</math>:  <math>\mathfrak F(\mathcal A)</math> (we use <tt>\mathfrak</tt>, which is consistent with the fact that <math>\finpowerset{\web{\mathcal A}}\subseteq \mathfrak F(\mathcal A) \subseteq\powerset{\web{\mathcal A}}</math>).
 == Miscellaneous ==

← Older revision		Revision as of 11:36, 6 September 2012
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	* [[Isomorphism]]: <math>A\cong B</math>		* [[Isomorphism]]: <math>A\cong B</math>
		+	* injection: <math>A\hookrightarrow B</math>
		+	* partial injection: <math>A\pinj B</math>

← Older revision		Revision as of 08:48, 19 October 2009
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	* Web of the finiteness space <math>\mathcal A</math>: <math>\web{\mathcal A}</math>		* Web of the finiteness space <math>\mathcal A</math>: <math>\web{\mathcal A}</math>
	* Finiteness structure of the space <math>\mathcal A</math>: <math>\mathfrak F(\mathcal A)</math> (we use <tt>\mathfrak</tt>, which is consistent with the fact that <math>\finpowerset{\web{\mathcal A}}\subseteq \mathfrak F(\mathcal A) \subseteq\powerset{\web{\mathcal A}}</math>).		* Finiteness structure of the space <math>\mathcal A</math>: <math>\mathfrak F(\mathcal A)</math> (we use <tt>\mathfrak</tt>, which is consistent with the fact that <math>\finpowerset{\web{\mathcal A}}\subseteq \mathfrak F(\mathcal A) \subseteq\powerset{\web{\mathcal A}}</math>).
		+
		+	== Miscellaneous ==
		+
		+	* [[Isomorphism]]: <math>A\cong B</math>

@@ Line 61: / Line 61: @@
 == Semantics ==
-=== Coherent spaces ===
+=== [[Coherent spaces]] ===
 * Web of the space <math>X</math>: <math>\web X</math>
 * Coherence relation of the space <math>X</math>: large <math>\coh_X</math> and strict <math>\scoh_X</math>

@@ Line 66: / Line 66: @@
 === [[Finiteness spaces]] ===
-* Web of the space <math>\mathcal A</math>: <math>\web {\mathcal A}</math>
+* Web of the finiteness space <math>\mathcal A</math>: <math>\web{\mathcal A}</math>
-* Finiteness structure of the space <math>\mathcal A</math>: <math>\mathfrak F(\mathcal A)</math>
+* Finiteness structure of the space <math>\mathcal A</math>:  <math>\mathfrak F(\mathcal A)</math> (we use <tt>\mathfrak</tt>, which is consistent with the fact that <math>\finpowerset{\web{\mathcal A}}\subseteq \mathfrak F(\mathcal A) \subseteq\powerset{\web{\mathcal A}}</math>).

← Older revision		Revision as of 14:41, 6 July 2009
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	* Web of the space <math>X</math>: <math>\web X</math>		* Web of the space <math>X</math>: <math>\web X</math>
	* Coherence relation of the space <math>X</math>: large <math>\coh_X</math> and strict <math>\scoh_X</math>		* Coherence relation of the space <math>X</math>: large <math>\coh_X</math> and strict <math>\scoh_X</math>
		+
		+	=== [[Finiteness spaces]] ===
		+	* Web of the space <math>\mathcal A</math>: <math>\web {\mathcal A}</math>
		+	* Finiteness structure of the space <math>\mathcal A</math>: <math>\mathfrak F(\mathcal A)</math>

← Older revision		Revision as of 15:19, 7 February 2009
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	Name of the connective, followed by some additional information if required, followed by "L" for a left rule or "R" for a right rule. This is for a two-sided system, "R" is implicit for one-sided systems.		Name of the connective, followed by some additional information if required, followed by "L" for a left rule or "R" for a right rule. This is for a two-sided system, "R" is implicit for one-sided systems.
	For example: <math>\wedge_1 \text{add} L</math>.		For example: <math>\wedge_1 \text{add} L</math>.
		+
		+	== Semantics ==
		+
		+	=== Coherent spaces ===
		+	* Web of the space <math>X</math>: <math>\web X</math>
		+	* Coherence relation of the space <math>X</math>: <math>\coh_X</math>

@@ Line 52: / Line 52: @@
 * First order quantification: <math>\forall x A</math> with substitution <math>A[t/x]</math>
 * Second order quantification: <math>\forall X A</math> with substitution <math>A[B/X]</math>
-* Quantification of arbitrary order (mainly first or second): <math>\forall\alpha A</math> with substitution <math>A[\tau/\alpha]</math>
+* Quantification of arbitrary order (mainly first or second): <math>\forall\xi A</math> with substitution <math>A[\tau/\xi]</math>
 === Rule names ===

@@ Line 56: / Line 56: @@
 === Rule names ===
-Name of the connective, followed by some additional information if required, followed by "L" for a left rule or "R" for a right rule.
+Name of the connective, followed by some additional information if required, followed by "L" for a left rule or "R" for a right rule. This is for a two-sided system, "R" is implicit for one-sided systems.
 For example: <math>\wedge_1 \text{add} L</math>.