u/rhizomed

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Proving: if every finite subgraph of G is k-colorable, then G is k-colorable.

For each vertex v, variables Pv,1,...,Pv,k ("v gets color i"). Axioms in Σ:

- Pv,1 ∨ ... ∨ Pv,k for each v

- ¬(Pv,i ∧ Pv,j) for i≠j

- ¬(Pu,i ∧ Pv,i) for each edge (u,v), each i

Σ satisfiable iff G is k-colorable. Every finite subset of Σ only mentions finitely many vertices/edges, and that induced finite subgraph is k-colorable by hypothesis, so every finite subset is satisfiable. By compactness, Σ is satisfiable, so G is k-colorable.

But isnt ropositional compactness is usually stated for countable languages? G could have uncountably many vertices, so Σ has uncountably many variables. Does compactness still hold as-is, or do I need the general version (via Zorn/ultrafilters) for uncountable Σ? If it still works, what's the justification? Thank you!

Today I went to a branch photography store in search for a camera. An assistant asks me if I need help and begins advertising.

He asks me if I'd like to see a demonstration and takes pictures, then, without asking, proceeds to take pictures of me and point the camera at my face.

I ask him not to and he says he wants to show me the colour science and skin tones. I say no and push the camera out of my face and it swung out of his hand but he had a strap attached to it so it hit the glass viewing table and damaged the front of the lens and lens hood. He starts yelling at me and calls for security. I told him I don't like my picture being taken and that he should've asked first. I ask him to delete the pictures and he deleted them in front of me.

I can't describe how hard I pushed his arm but I'm really sensitive about my appearance and was shocked because I said no in front of him and he still took pictures of me.

He says that there's security cameras recording me anyway and that they have the right to photograph people in their store. Security intervenes and asks what's going on, the staff member explains and they review the footage and ask me to give my details. I gave fake details and left the store. I was wondering what legal action I may be susceptible to and whether I have any grounds to have the staff member investigated. I'm worried they'll be able to identify me because of my face on security. I didn't get to see security footage myself.

hey! I'm a new yorker that's been living in the UK for 7 years, mainly because of academia. I've just finished my PhD in philosophy/modal logic and I couldn't be more excited.

Some more about me: I'm a very artsy/reading/deep discussion type of person. I highly value intelligence (who doesn't?) but I am specially looking for people are well-read and push discussions about the world and how it functions. That being said, I have so many interests:

philosophy: modal logic, analytic, phil of science, free will, personal identity, Hegel, deleueze

other: critical theory, jung, marx, bourdieu. any analyses of gender, class, etc. music / media: radiohead, CAS, comics, batman beyond, hotd, Evangelion

When I'm not scribbling in my notebooks, you can catch me bouldering/rock climbing, thrifting or putting together outfits or hiking. I used to be super into beauty photography if you can re-ignite that passion. I strike a strange pendulum of being inside 24/7 to outside 24/7, so I also play games like valorant and deadlock.

I am only looking for people who are deeply moved by these topics, and can generate their own opinions. I think it's clear if you feign interest in them you'll be wasting both of our times. So please start off with a discussion!

Finally, I'm someone who wishes the world to a be a better place when I leave it. and I would like my partner to share this by being someone who is progressive, a good listener, considerate and kind.

See you!

hi,

im a student that has some time off. I haven't played val or deadlock in over a year so I'm like gold/plat. i really enjoy both games so looking for some friends to grind ranked with. i dont take it too seriously though as i have to study too

- preferably women (you will get blocked instantly if you are looking for a relationship).

- im friendly and don't want to duo with anyone toxic

- 20+

im generally a listener and can hear you yap about your day or we can play quietly. i hobbies in climbing, philosophy, reading, hiking and art

I returned back to education at 21, so I didn't feel like I was that much older than them. But the maturity gap felt kinda apparent, I also went to cambridge and it was so much studying and not a lot of fun. I get I chose it but I kinda feel robbed of the uni experience mainly because the post grads were about my age but i didnt see them regularly

I play a lot of valorant / deadlock right now, I have big summer break from university. I'm super chill and don't care about winning that much but would love some friends to play ranked with.

I'm plat in val and deadlock pretty new, under 40hrs - but I really do love it

im also a great listener if anyones a yapper! or you can listen to me rant about my PhD

hi, I'm from the US and I'm a visiting student here for my PhD.

I'm interested in art, film, philosophy, and UX design, running and climbing. I love music too and am always down for anything - generally very positive and just making the most out of life. will listen to your strange stories with a lot of head nods.

would love potentially some platonic friends/girls to enjoy london with!