Am I assigning ordinals to this group correctly? I've been studying ordinal numbers and I'm trying to use them to totally order the elements of a countable, artinian, but not noetherian group $(G,\cdot)$ which is simply generated as follows: There is a single identity element $e$, and for e...

It is very well known that there are $12$ pentominos and they can tile $6 \times 10$, $5 \times 12$, $4 \times 15$ and $3 \times 20$ rectangles. Now, let's define a function for simplify this. $$t(n)=\begin{cases} 1, & \text{if $n$-ominos tile rectangle} \\ 0 & \text{else} \end{cases}$$ $t(5)=0$...

We are given a matrix $$ A = \begin{bmatrix} 3 & 0 & -1 \\ -1 & 4 & -3 \\ -1 & 0 & 5 \\ \end{bmatrix} $$ and we are asked to find a matrix $P$ such that $P^{-1}AP$ is upper triangular. Here, we first find one eigenvalue as $\lambda= 4$. Then the matrix $$ A-4I = ...

I'm studying Chow Varieties from the book. In order to show that the set $\mathcal{C}_{k-1,d}$ of $(k-1)$-dimensional cycles supported in $\mathbb{P}^{n-1}$ is indeed a variety we have to characterize Chow Forms, that is we want know when an hypersurface of $G(n-k,n)$ is a the associated hypersu...

I read a lot about Linear Logic recently but I failed to find any real use to the logic. I'd like to know how and where Linear Logic could be applied. Something like lambda calculus can be clearly used as a programming language (scheme, lisp). But I don't see how Linear Logic could be used in th...

Linear logic abandons the structural rules of weakening and contraction. I wanted to know whether we have $p ⊸ p$ in linear logic. Can anyone help?

Is there any correct book/textbook/pdf to understand what is linear logic ? I do research in (standard) logic/model theory, so I'm totally ok with a text which assumes mathematical maturity.

Why is it called "Linear" Logic? What's linear about it?

I am looking for an introduction to the model theory of Linear Logic. Can you recommend any clear introductions? I am particularly interested in those models that regard coherence spaces.

Is it possible to define a negation in intuitionistic linear logic, the way one does in intuitionistic logic, i.e. $A^{\bot} \equiv A \multimap \mathbf{0}$ (or, as it would be written in intuitionistic logic, $\neg A \equiv A \to \bot$)? While I can prove, e.g. the theorem... $$A^{\bot\bot}\otim...

How do we obtain the equivalence $A \otimes 0 \equiv 0$ and its dual in linear logic? Are they a consequence of cut-elimination? I found them listed as basic equivalences in the following resource: http://iml.univ-mrs.fr/~lafont/pub/llpages.pdf , but have not found an explicit way of proving it ...

Let $\mathcal{C}$ be a symmetric monoidal closed category. My question is the following: Given three objects $X$, $Y$ and $Z$, and a morphism $f \colon Y \to Z$ in $\mathcal{C}$, does it necessarily exist a morphism from $X \multimap Y$ to $X \multimap Z$ in $\mathcal{C}$? By $X \multimap Y...

A tableaux method for linear logic is briefly discussed in https://www.academia.edu/6591354/TABLEAU_METHODS_FOR_SUBSTRUCTURAL_LOGICS?auto=download D'Agostino writes (p.418-9): ''It is straightforward to translate the Linear Logic deductive policy into a stricter criterion of use: a Li...

The positive exponential ! has a very satisfying interpretation in terms of the standard resource interpretation of linear logic. Given a resource $a$, we know that $!a$ means an infinite supply of $a$. Or, stated more concretely in terms of the connectives of linear logic: $!a \equiv !a \otimes ...

Every presentation of linear logic I've seen seems to either omit or treat quantifiers as an after-thought. Even Girard says that there is "little to say" about them. However, if we view universal (existential) quantification as a generalization of conjunction (disjunction), then we would expec...