My Landlord won't fix my AC if it "costs too much"

Location: California

The AC that came with my studio is leaking and stopped working. They're telling me that they'll get someone to come look at it but that technically they're not legally viable to "provide cooling". It gets to more than 100 degrees in my studio. I've been suffering in my shed all summer because the AC isn't really working, I want to know if I can get them to fix it no matter the price.

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EDIT: they're no longer offering to fix it or having someone to come check it out. Please help :(

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UPDATE Sep25th 12pm: I read my lease like someone has suggested, I REALLY wish I could put a picture here but I guess I'm gonna have to type it out :(, but this is the only thing that mentioned air conditioning in the lease!

XXXI. MAINTENANCE, REPAIRS, OR ALTERATIONS. The Tenant shall, at their own expense and at all times,maintaine premises in a clean and sanitary manner, and shall surrender the same at termination hereof, in as good condition as received, normal wear and tear excepted. The Tenant may not make any alterations to the leased premises without the consent in writing of the Landlord. The Landlord shall be responsible for repairs to the interior and exterior of the building. If the Premises includes a washer, dryer, freezer, dehumidifier unit and/or air conditioning unit, the Landlord makes no warranty as to the repair or replacement of units if one or all shall fail to operate. The Landlord will place fresh batteries in all battery operated smoke detectors when the tenant moved into the premises. After the initial placement of the fresh batteries is the responsibility of the Tenant to replace batteries when needed. A monthly "cursory" inspection may be required for all fire extinguishers to make sure they are fully charged.

Author: Commercial_Road664